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The partial sum process of orthogonal expansion as geometric rough process with Fourier series as an example---an improvement of Menshov-Rademacher theorem

Abstract:
In this paper, we prove that the partial sum process of general orthogonal series is a geometric 2-rough process under the same condition as in Menshov-Rademacher Theorem. For Fourier series, the condition can be improved, and an equivalent condition on the limit function is identified.
Publication status:
Published

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Publisher copy:
10.1016/j.jfa.2013.08.032

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
JOURNAL OF FUNCTIONAL ANALYSIS
Volume:
265
Issue:
12
Pages:
3067-3103
Publication date:
2011-09-06
DOI:
ISSN:
0022-1236
URN:
uuid:54a7200b-eebc-49b4-ac68-2c41ca1a5270
Source identifiers:
366679
Local pid:
pubs:366679
Keywords:

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